To choose the appropriate simulation method for evaluating the football team's 17% chance of scoring on the final play of the game, we need to match this scoring probability as closely as possible to a probabilistic event in one of the given devices and methods.
Let's analyze each option in detail:
1. Flipping a coin and recording heads:
- Probability Analysis: The probability of flipping a coin and it landing heads (or tails) is 50%, which is significantly higher than 17%.
- Conclusion: This method is not suitable since 50% does not approximate 17%.
2. Rolling a die and recording the occurrence of rolling a 2:
- Probability Analysis: A standard die has 6 faces, each with an equal chance of occurring. Therefore, the probability of rolling a 2 is [tex]\( \frac{1}{6} \approx 0.1667 \)[/tex] or approximately 16.67%.
- Conclusion: This probability is very close to the desired 17%, making this method the closest option.
3. Spinning a spinner and recording when it lands on 3:
- Probability Analysis: The effectiveness of this method depends on the design of the spinner. If the spinner is equally divided into 10 parts, the probability would be [tex]\( \frac{1}{10} = 10\%\)[/tex]. For other divisions, the probability will differ.
- Conclusion: The 10% probability is not close enough to the 17% target, making it a less suitable option without more specific details on the spinner’s division.
4. Picking and replacing items with recording the probability of picking a red item:
- Probability Analysis: This method relies on the specific distribution of colored items. Without additional details specifying a distribution that approximates 17%, it's not possible to conclude this is a suitable method.
- Conclusion: Unspecified distributions cannot guarantee the needed 17% probability.
Given these analyses, the most appropriate simulation method is:
Rolling a die and recording the occurrence of rolling a 2.
This method's [tex]\( \frac{1}{6} \)[/tex] chance closely approximates the football team's 17% chance of scoring. Therefore, in 100 trials, this method would provide a reasonable simulation of the scoring probability.
